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Published online by Cambridge University Press: 25 May 2016
Cosmological lens statistics was studied first by Turner, Ostriker, & Gott (1984), and developed by Hinshaw & Krauss (1987), Gott, Park, & Lee (1989), Turner (1990), Krauss & White (1992), and Wallington & Narayan (1993). The expected number of lensed quasars in general quasar catalogs was examined by Fukugita & Turner (1991), Kochanek (1991), and Fukugita et al. (1992), and the number expected in the HST Snapshot Survey (Bahcall et al. 1992, Maoz et al. 1992, 1993) was examined by Maoz & Rix (1939) and Kochanek (1993). In most of these studies, galaxies were assumed to be the lenses, and clusters of galaxies played only auxiliary roles. As a result, the expected number of lensed quasars with separations larger than 3 arcsec is negligibly small compared to the total number of lenses. However, about 33% of observed lensed quasars have image separations larger than 3 arcsec (Maoz et al. 1993, Refsdal & Surdej 1994). This observational fact is very important.